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A338125 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance 2w apart where the walk starts at the middle point between the planes.

%I A338125 #16 Oct 14 2020 23:16:15
%S A338125 6,28,30,124,148,150,516,692,724,726,2156,3196,3492,3532,3534,8804,
%T A338125 14324,16428,16876,16924,16926,36388,64076,76956,80700,81332,81388,
%U A338125 81390,148452,282716,354740,380964,387052,387900,387964,387966,609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886
%N A338125 Triangle read by rows: T(n,w) is the number of n-step self avoiding walks on a 3D cubic lattice confined between two infinite planes a distance 2w apart where the walk starts at the middle point between the planes.
%H A338125 Scott R. Shannon, <a href="/A338125/a338125.txt">Full data table for n=1 to n=15</a>.
%F A338125 For w>=n, T(n,w) = A001412(n).
%e A338125 T(2,1) = 28 as after a step in one of the two directions towards the planes the walk must turn along the plane; this eliminates the 2-step straight walk in those two directions, so the total number of walks is A001412(2) - 2 = 30 - 2 = 28.
%e A338125 The table begins:
%e A338125 6;
%e A338125 28,30;
%e A338125 124,148,150;
%e A338125 516,692,724,726;
%e A338125 2156,3196,3492,3532,3534;
%e A338125 8804,14324,16428,16876,16924,16926;
%e A338125 36388,64076,76956,80700,81332,81388,81390;
%e A338125 148452,282716,354740,380964,387052,387900,387964,387966;
%e A338125 609812,1251044,1631420,1795212,1843452,1852716,1853812,1853884,1853886;
%e A338125 2478484,5493804,7431100,8377908,8712892,8795020,8808420,8809796,8809876,8809878;
%Y A338125 Cf. A338126 (start on a plane), A001412 (w->infinity), A001412, A337023, A337400, A039648.
%K A338125 nonn,tabl
%O A338125 1,1
%A A338125 _Scott R. Shannon_, Oct 11 2020